Subgroups — C₁₉×#24995 #18030954

Order 4864.

638 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2582	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2355	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2101	C₂	1	2	yes	maximal
4	C₁₉×#2074	C₂	1	2	yes	maximal
5	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1928	C₂	1	2	yes	maximal
8	C₁₉×#1918	C₂	1	2	yes	maximal
9	C₁₉×#1834	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#107	C₂²	1	2	yes	—
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#103	C₂²	1	2	yes	—
18	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#398	—	2	2	no	—
21	C₁₉×#391	—	2	1	no	—
22	C₁₉×#391	—	2	1	no	—
23	C₁₉×#391	C₂²	1	2	yes	—
24	C₁₉×#389	—	2	1	no	—
25	C₁₉×#389	C₂²	1	2	yes	—
26	C₁₉×#387	—	2	2	no	—
27	C₁₉×#384	C₂²	1	1	yes	characteristic
28	C₁₉×#384	C₂²	1	1	yes	characteristic
29	C₁₉×#382	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#340	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	1	yes	characteristic
39	C₁₉×#336	C₂²	1	2	yes	—
40	C₁₉×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
46	C₄×Q₈×C₁₉	—	2	2	no	—
47	C₄×Q₈×C₁₉	—	2	2	no	—
48	C₄×Q₈×C₁₉	—	2	2	no	—
49	C₄×Q₈×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	—	2	1	no	—
65	C₂×C₄²×C₁₉	—	2	2	no	—
66	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₁₉×#107	—	2	4	no	—
69	C₁₉×C₄⋊C₈	—	2	2	no	—
70	C₁₉×#103	—	2	4	no	—
71	C₁₉×#103	—	2	2	no	—
72	C₁₉×#103	—	2	2	no	—
73	C₄×C₈×C₁₉	—	2	2	no	—
74	C₁₉×#95	—	2	2	no	—
75	C₁₉×#95	—	2	1	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₁₉×#95	—	2	2	no	—
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	1	no	—
88	C₂×Q₈×C₁₉	—	2	1	no	—
89	C₂×Q₈×C₁₉	#41	1	2	yes	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₁₉	—	2	1	no	—
102	C₂×C₈×C₁₉	—	2	1	no	—
103	C₂×C₈×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	2	1	no	—
105	C₂×C₈×C₁₉	—	2	1	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	1	no	—
109	C₂×C₈×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	4	2	no	—
122	C₄⋊C₄×C₁₉	—	4	2	no	—
123	C₄⋊C₄×C₁₉	—	4	2	no	—
124	C₄⋊C₄×C₁₉	—	8	1	no	—
125	C₄⋊C₄×C₁₉	—	8	1	no	—
126	C₄⋊C₄×C₁₉	—	8	2	no	—
127	C₄⋊C₄×C₁₉	#41	1	2	yes	—
128	C₄²×C₁₉	—	2	2	no	—
129	C₄²×C₁₉	—	2	2	no	—
130	C₄²×C₁₉	—	4	2	no	—
131	C₄²×C₁₉	—	4	2	no	—
132	C₄²×C₁₉	—	8	2	no	—
133	C₄²×C₁₉	#41	1	2	yes	—
134	C₄²×C₁₉	#41	1	2	yes	—
135	#24995	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₁₉	—	2	2	no	—
138	Q₈×C₁₉	—	2	2	no	—
139	Q₈×C₁₉	—	4	1	no	—
140	Q₈×C₁₉	—	4	1	no	—
141	Q₈×C₁₉	—	4	4	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	#123	1	2	yes	—
169	C₂×C₄×C₁₉	#123	1	2	yes	—
170	C₂×C₄×C₁₉	#135	1	2	yes	—
171	C₂×C₄×C₁₉	#137	1	2	yes	—
172	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
178	C₈×C₁₉	—	4	2	no	—
179	C₈×C₁₉	—	4	1	no	—
180	C₈×C₁₉	—	4	1	no	—
181	#2582	C₂×C₁₉	1	1	yes	characteristic
182	#2355	C₂×C₁₉	1	1	yes	characteristic
183	#2101	C₂×C₁₉	1	2	yes	—
184	#2074	C₂×C₁₉	1	2	yes	—
185	#1984	C₂×C₁₉	1	1	yes	characteristic
186	#1947	C₂×C₁₉	1	1	yes	characteristic
187	#1928	C₂×C₁₉	1	2	yes	—
188	#1918	C₂×C₁₉	1	2	yes	—
189	#1834	C₂×C₁₉	1	1	yes	characteristic
190	#1803	C₂×C₁₉	1	1	yes	characteristic
191	C₄×#103	C₂×C₁₉	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
193	C₂²×C₁₉	#548	1	1	yes	characteristic
194	C₂²×C₁₉	#548	1	1	yes	characteristic
195	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
196	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
197	C₂²×C₁₉	#576	1	1	yes	characteristic
198	C₂²×C₁₉	#578	1	1	yes	characteristic
199	C₄×C₁₉	—	2	2	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	—	4	2	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	8	1	no	—
205	C₄×C₁₉	—	8	2	no	—
206	C₄×C₁₉	—	8	1	no	—
207	C₄×C₁₉	—	8	2	no	—
208	C₄×C₁₉	#485	1	4	yes	—
209	C₄×C₁₉	#529	1	1	yes	characteristic
210	C₄×C₁₉	#541	1	1	yes	characteristic
211	C₄×C₁₉	#552	1	1	yes	characteristic
212	C₄×C₁₉	#556	1	1	yes	characteristic
213	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
215	C₂×#107	C₂²×C₁₉	1	2	yes	—
216	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×#103	C₂²×C₁₉	1	2	yes	—
218	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
219	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
221	#398	—	2	2	no	—
222	#391	—	2	1	no	—
223	#391	—	2	1	no	—
224	#391	C₂²×C₁₉	1	2	yes	—
225	#389	—	2	1	no	—
226	#389	C₂²×C₁₉	1	2	yes	—
227	#387	—	2	2	no	—
228	#384	C₂²×C₁₉	1	1	yes	characteristic
229	#384	C₂²×C₁₉	1	1	yes	characteristic
230	#382	C₂²×C₁₉	1	2	yes	—
231	C₄×C₄⋊C₄	—	2	1	no	—
232	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
233	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
234	#340	C₂²×C₁₉	1	2	yes	—
235	#340	C₂²×C₁₉	1	2	yes	—
236	#340	C₂²×C₁₉	1	2	yes	—
237	#340	C₂²×C₁₉	1	2	yes	—
238	#340	C₂²×C₁₉	1	1	yes	characteristic
239	#340	C₂²×C₁₉	1	1	yes	characteristic
240	#336	C₂²×C₁₉	1	2	yes	—
241	#336	C₂²×C₁₉	1	2	yes	—
242	C₂×C₁₉	#2421	1	1	yes	characteristic
243	C₂×C₁₉	C₂×#485	1	1	yes	characteristic
244	C₂×C₁₉	#3098	1	1	yes	characteristic
245	C₂×C₁₉	#3361	1	1	yes	characteristic
246	C₂×C₁₉	#3364	1	1	yes	characteristic
247	C₂×C₁₉	#3374	1	1	yes	characteristic
248	C₂×C₁₉	#3375	1	1	yes	characteristic
249	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
250	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	—	2	2	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
265	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
275	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
276	#107	—	2	4	no	—
277	C₄⋊C₈	—	2	2	no	—
278	#103	—	2	4	no	—
279	#103	—	2	2	no	—
280	#103	—	2	2	no	—
281	C₄×C₈	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	1	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	C₁₉	#24995	1	1	yes	characteristic, direct product factor, Sylow
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	#41×C₁₉	1	2	yes	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
309	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	8	1	no	—
334	C₄⋊C₄	—	8	1	no	—
335	C₄⋊C₄	—	8	2	no	—
336	C₄⋊C₄	#41×C₁₉	1	2	yes	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	4	2	no	—
340	C₄²	—	4	2	no	—
341	C₄²	—	8	2	no	—
342	C₄²	#41×C₁₉	1	2	yes	—
343	C₄²	#41×C₁₉	1	2	yes	—
344	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	4	4	no	—
348	Q₈	—	4	1	no	—
349	Q₈	—	4	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	C₁₉×#123	1	2	yes	—
377	C₂×C₄	C₁₉×#123	1	2	yes	—
378	C₂×C₄	C₁₉×#135	1	2	yes	—
379	C₂×C₄	C₁₉×#137	1	2	yes	—
380	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
382	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
383	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
384	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
385	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
386	C₈	—	4	2	no	—
387	C₈	—	4	1	no	—
388	C₈	—	4	1	no	—
389	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
390	C₂²	C₁₉×#548	1	1	yes	characteristic
391	C₂²	C₁₉×#548	1	1	yes	characteristic
392	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
393	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
394	C₂²	C₁₉×#576	1	1	yes	characteristic
395	C₂²	C₁₉×#578	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	8	1	no	—
404	C₄	—	8	2	no	—
405	C₄	C₁₉×#485	1	4	yes	—
406	C₄	C₁₉×#529	1	1	yes	characteristic
407	C₄	C₁₉×#541	1	1	yes	characteristic
408	C₄	C₁₉×#552	1	1	yes	characteristic
409	C₄	C₁₉×#556	1	1	yes	characteristic
410	C₂	C₁₉×#2421	1	1	yes	characteristic
411	C₂	C₂×C₁₉×#485	1	1	yes	characteristic
412	C₂	C₁₉×#3098	1	1	yes	characteristic
413	C₂	C₁₉×#3361	1	1	yes	characteristic
414	C₂	C₁₉×#3364	1	1	yes	characteristic
415	C₂	C₁₉×#3374	1	1	yes	characteristic
416	C₂	C₁₉×#3375	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
135. #24995	C₁₉	direct (N × H)
289. C₁₉	#24995	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#2582	2
C₁₉×#2355	2
C₁₉×#2101	2
C₁₉×#2074	2
C₁₉×#1984	2
C₁₉×#1947	2
C₁₉×#1928	2
C₁₉×#1918	2
C₁₉×#1834	2
C₁₉×#1803	2
C₄×C₁₉×#103	2
#24995	19

Subgroups — C19×#24995 #18030954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24995 #18030954